Best proximity point results for almost contraction and application to nonlinear differential equation

Hussain A., Abbas M., Adeel M., Kanwal T.

Sahand Communications in Mathematical Analysis, vol.17, no.2, pp.119-138, 2020 (ESCI, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 17 Issue: 2
  • Publication Date: 2020
  • Doi Number: 10.22130/scma.2019.95982.515
  • Journal Name: Sahand Communications in Mathematical Analysis
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, zbMATH, Directory of Open Access Journals
  • Page Numbers: pp.119-138
  • Keywords: Almost contraction, Best proximity points, Differential equation, Θ-contraction
  • Uşak University Affiliated: No

Abstract

Berinde [V. Berinde, Approximating fixed points of weak contractions using the Picard iteration, Nonlinear Anal. Forum 9 (2004), 43-53] introduced almost contraction mappings and proved Banach contraction principle for such mappings. The aim of this paper is to introduce the notion of multivalued almost Θ-contraction mappings and to prove some best proximity point results for this new class of mappings. As applications, best proximity point and fixed point results for weak single valued Θ-contraction mappings are obtained. Moreover, we give an example to support the results presented herein. An application to a nonlinear differential equation is also provided.